The "rotate 2" works as:
1, rotate by angle a (as specified in the rotate 2 dialog) around "absolute reference point" (point A);
2, rotate by angle b around "relative reference point"(point B);
two subsequent rotations are equivalent to one rotation and displacement.
using complex number to denote points in a plane, the rotate 2 modifies a point z to:
step 1, z is rotated around c by angle a, and the result is
A + (z - A) exp(i a);
step 2, the result from step 1 is rotated around d by angle b, and the result is
B +( A + (z - A) exp(i a) - B) exp( i b) = B + (A -B) exp( ib) - A exp( i (a+b) ) + z exp( i (a+b) )
there's an offset part B + (A -B) exp( ib) - A exp( i (a+b) ) and a rotate part z exp( i (a+b) ).
special cases
if A=B, i.e., around the same center:
A + (z-A) exp( i (a+b) ). this is the same as rotation around center by angle a+b;
if a+b =0, i.e., rotate by a around the first center, followed by -a rotation around the second center.
(B -A)(1- exp( ib)) + z
it's a offset from the position of B rotated around A by -a, to the position of B.
Quenzo wrote
Hi, I have not found any post about this issue, so it seems appropriate to open a new thread, if there is any open, I apologize in advance
I don't understand the utility of "Specify relative reference point" in the Rotate two option.
When it asks (in command line) "Specify absolute reference point" we give coordinates to the application and it locates a center point of rotation around which will rotate entities, but when it asks "Specify relative reference point" the point that we give, has no effect on the drawing.
I've tried a lot of times, and there may be changes in the location of the central point when passing the coordinate such as relative (eg. @ 12,30) when the application asked "Specify absolute reference point", but when it asked "Specify relative reference point" and we give a coordinate, absolutely nothing happens.
If anyone in the forum know why this happens, I appreciate the help
Regards
Locked
Oct 04, 2014; 6:44pm
